Finite Group Databasebeta

← #2081×C151 #34065413

Subgroups — #2081×C151 #34065413

Order 19328.

204 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#430×C151C211yesmaximal, characteristic, complemented
2#418×C151C211yesmaximal, characteristic
3#418×C151C211yesmaximal, characteristic
4C2×#100×C151C211yesmaximal, characteristic
5#344×C151C211yesmaximal, characteristic, complemented
6#344×C151C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C151C211yesmaximal, characteristic, complemented
8C22×D4×C151C2211yescharacteristic
9C2×M16×C151C2211yescharacteristic
10C2×M16×C151C2211yescharacteristic
11C2×M16×C151C2211yescharacteristic
12C2×M16×C151C2211yescharacteristic
13#117×C151C2211yescharacteristic
14#117×C151C2211yescharacteristic
15#108×C151—22no—
16#102×C151—22no—
17#102×C151—22no—
18#100×C151—22no—
19C24×C151—21no—
20C2×D4×C151—21no—
21C2×D4×C151—21no—
22C2×D4×C151—21no—
23C2×D4×C151—21no—
24C2×D4×C151—21no—
25C2×D4×C151D412yes—
26C22×C4×C151C2311yescharacteristic
27M16×C151—21no—
28M16×C151—21no—
29M16×C151—21no—
30M16×C151—21no—
31M16×C151—21no—
32M16×C151—21no—
33M16×C151—21no—
34M16×C151—21no—
35C2×C8×C151—21no—
36C2×C8×C151—21no—
37C2×C8×C151—21no—
38C2×C8×C151D412yes—
39C4⋊C4×C151—21no—
40C4⋊C4×C151—21no—
41C22⋊C4×C151—21no—
42C22⋊C4×C151—21no—
43C42×C151—21no—
44C42×C151—21no—
45C23×C151—22no—
46C23×C151—41no—
47C23×C151—41no—
48C23×C151—82no—
49C23×C151#4111yescharacteristic
50D4×C151—22no—
51D4×C151—22no—
52D4×C151—41no—
53D4×C151—41no—
54C2×C4×C151—41no—
55C2×C4×C151—41no—
56C2×C4×C151C2×D411yescharacteristic
57C2×C4×C151C2×D411yescharacteristic
58C2×C4×C151#4111yescharacteristic
59C2×C4×C151#4111yescharacteristic
60C2×C4×C151#4111yescharacteristic
61C2×C4×C151#4111yescharacteristic
62C8×C151—22no—
63C8×C151—41no—
64C8×C151—41no—
65C8×C151—41no—
66C22×C151—41no—
67C22×C151—42no—
68C22×C151—82no—
69C22×C151—82no—
70C22×C151—82no—
71C22×C151#12311yescharacteristic
72C22×C151#12411yescharacteristic
73C22×C151#12611yescharacteristic
74C4×C151—81no—
75C4×C151—81no—
76C4×C151#12111yescharacteristic
77C4×C151#12311yescharacteristic
78C4×C151#12311yescharacteristic
79C4×C151#12611yescharacteristic
80C2×C151—21no—
81C2×C151—21no—
82C2×C151—21no—
83C2×C151—82no—
84C2×C151#39711yescharacteristic
85C151#208111yescharacteristic, direct product factor, Sylow
86#2081C15111yesmaximal, characteristic, direct product factor, Sylow
87#430C2×C15111yescharacteristic, complemented
88#418C2×C15111yescharacteristic
89#418C2×C15111yescharacteristic
90C2×#100C2×C15111yescharacteristic
91#344C2×C15111yescharacteristic, complemented
92#344C2×C15111yescharacteristic, complemented
93H(3,ℤ/4)C2×C15111yescharacteristic, complemented
94C22×D4C22×C15111yescharacteristic
95C2×M16C22×C15111yescharacteristic
96C2×M16C22×C15111yescharacteristic
97C2×M16C22×C15111yescharacteristic
98C2×M16C22×C15111yescharacteristic
99#117C22×C15111yescharacteristic
100#117C22×C15111yescharacteristic
101#108—22no—
102#102—22no—
103#102—22no—
104#100—22no—
105C24—21no—
106C2×D4—21no—
107C2×D4—21no—
108C2×D4—21no—
109C2×D4—21no—
110C2×D4—21no—
111C2×D4D4×C15112yes—
112C22×C4C23×C15111yescharacteristic
113M16—21no—
114M16—21no—
115M16—21no—
116M16—21no—
117M16—21no—
118M16—21no—
119M16—21no—
120M16—21no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8D4×C15112yes—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C22⋊C4—21no—
128C22⋊C4—21no—
129C42—21no—
130C42—21no—
131C23—22no—
132C23—41no—
133C23—41no—
134C23—82no—
135C23#41×C15111yescharacteristic
136D4—22no—
137D4—22no—
138D4—41no—
139D4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4C2×D4×C15111yescharacteristic
143C2×C4C2×D4×C15111yescharacteristic
144C2×C4#41×C15111yescharacteristic
145C2×C4#41×C15111yescharacteristic
146C2×C4#41×C15111yescharacteristic
147C2×C4#41×C15111yescharacteristic
148C8—22no—
149C8—41no—
150C8—41no—
151C8—41no—
152C22—41no—
153C22—42no—
154C22—82no—
155C22—82no—
156C22—82no—
157C22#123×C15111yescharacteristic
158C22#124×C15111yescharacteristic
159C22#126×C15111yescharacteristic
160C4—81no—
161C4—81no—
162C4#121×C15111yescharacteristic
163C4#123×C15111yescharacteristic
164C4#123×C15111yescharacteristic
165C4#126×C15111yescharacteristic
166C2—21no—
167C2—21no—
168C2—21no—
169C2—82no—
170C2#397×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#397
commutator, Frattini, cosocleC22×C4C23×C151
prime radicalC22×D4×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C22×C4×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #430×C151C2semidirect
5. #344×C151C2semidirect
6. #344×C151C2semidirect
7. H(3,ℤ/4)×C151C2semidirect
85. C151#2081direct (N × H)
86. #2081C151direct (N × H)
87. #430C2×C151semidirect
91. #344C2×C151semidirect
92. #344C2×C151semidirect
93. H(3,ℤ/4)C2×C151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#430×C1512
#418×C1512
C2×#100×C1512
#344×C1512
H(3,ℤ/4)×C1512
#2081151